Biharmonic - Revision history

Guillaume at 14:30, 28 June 2011

2011-06-28T14:30:02Z

2011-06-28T14:29:09Z

2011-06-28T14:28:34Z

2011-06-28T14:26:58Z

2011-06-28T14:26:38Z

2011-06-28T14:22:07Z

2011-06-28T14:21:13Z

2011-06-28T14:20:50Z

2011-06-28T14:18:34Z

2011-06-28T14:17:26Z

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 where <math>\mathrm{K}</math> is Fick's law diffusivity.
-A ready made formula that would estimate the order of magnitude of the <math>\kappa_4</math> coefficient would be
+A ready made formula that would estimate the order of magnitude of the <math>\kappa_4</math> coefficient for momentum would be
 <math>\kappa_4 \sim \frac{U}{16} \Delta x^3</math>

← Older revision		Revision as of 14:29, 28 June 2011
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−	The biharmonic filter is an extra term that is added in the horizontal turbulent viscous flux, '''J''', that filters high frequency oscillations in a numerical model of advection-diffusion of a property <math>C</math>(i.e. oscillations with a wave-length equal to one or two widths of the horizontal resolution):	+	The biharmonic filter is an extra term that is added in the horizontal turbulent viscous flux, '''J''', that filters high frequency oscillations in a numerical model of advection-diffusion of a property <math>C</math>(i.e. oscillations with a wave-length equal to one or two widths of the horizontal resolution):

	<math>\mathrm{J} = -\mathrm{K}\cdot \nabla C + \nabla_{h}\left( \kappa_4 \nabla_{h}^2 C \right) </math>		<math>\mathrm{J} = -\mathrm{K}\cdot \nabla C + \nabla_{h}\left( \kappa_4 \nabla_{h}^2 C \right) </math>

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-The biharmonic filter is an extra term that is added to the horizontal turbulent viscous flux, '''J''', that filters high frequency oscillations in a numerical model of advection-diffusion (i.e. oscillations with a wave-length equal to one or two widths of the horizontal resolution):
+The biharmonic filter is an extra term that is added in the horizontal turbulent viscous flux, '''J''', that filters high frequency oscillations in a numerical model of advection-diffusion of a property <math>C</math>(i.e. oscillations with a wave-length equal to one or two widths of the horizontal resolution):
 <math>\mathrm{J} = -\mathrm{K}\cdot \nabla C + \nabla_{h}\left( \kappa_4 \nabla_{h}^2 C \right) </math>
 A ready made formula that would estimate the order of magnitude of the <math>\kappa_4</math> coefficient would be

← Older revision		Revision as of 14:26, 28 June 2011
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−	The biharmonic ~~coefficient~~ is an extra term that is added to the horizontal turbulent viscous flux, '''J''', that filters high frequency oscillations in a numerical model of advection-diffusion (i.e. oscillations with a wave-length equal to one or two widths of the horizontal resolution):	+	The biharmonic filter is an extra term that is added to the horizontal turbulent viscous flux, '''J''', that filters high frequency oscillations in a numerical model of advection-diffusion (i.e. oscillations with a wave-length equal to one or two widths of the horizontal resolution):

	<math>\mathrm{J} = -\mathrm{K}\cdot \nabla C + \nabla_{h}\left( \kappa_4 \nabla_{h}^2 C \right) </math>		<math>\mathrm{J} = -\mathrm{K}\cdot \nabla C + \nabla_{h}\left( \kappa_4 \nabla_{h}^2 C \right) </math>

← Older revision		Revision as of 14:26, 28 June 2011
Line 1:		Line 1:
−	The biharmonic coefficient is an extra term that is added to the horizontal turbulent viscous flux, '''J''':	+	The biharmonic coefficient is an extra term that is added to the horizontal turbulent viscous flux, '''J''', that filters high frequency oscillations in a numerical model of advection-diffusion (i.e. oscillations with a wave-length equal to one or two widths of the horizontal resolution):

	<math>\mathrm{J} = -\mathrm{K}\cdot \nabla C + \nabla_{h}\left( \kappa_4 \nabla_{h}^2 C \right) </math>		<math>\mathrm{J} = -\mathrm{K}\cdot \nabla C + \nabla_{h}\left( \kappa_4 \nabla_{h}^2 C \right) </math>

← Older revision		Revision as of 14:22, 28 June 2011
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	Delhez, E., & Deleersnijder, E. (2007). Overshootings and spurious oscillations caused by biharmonic mixing.		Delhez, E., & Deleersnijder, E. (2007). Overshootings and spurious oscillations caused by biharmonic mixing.
	Ocean Modelling, 17(3), 183-198. doi: 10.1016/j.ocemod.2007.01.002.		Ocean Modelling, 17(3), 183-198. doi: 10.1016/j.ocemod.2007.01.002.
		+
		+	[[Category:MOHID]]
		+	[[Category:Hydrodynamic]]

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 where U is a typical flow velocity and <math>\Delta x</math> is the numerical model horizontal resolution.
 ==References==
   Delhez, E., & Deleersnijder, E. (2007). Overshootings and spurious oscillations caused by biharmonic mixing.
   Ocean Modelling, 17(3), 183-198. doi: 10.1016/j.ocemod.2007.01.002.